How does the change in the sample size affect the outcome of the hypothesis test?

Q. What are adaptive clinical trials?

Adaptive trials are any trial where a change or decision is made to a trial while it is still on-going. Adaptive trials enable continual modification to the trial design based on interim data which in turn can allow you to explore options and treatments that you would otherwise be unable to which can lead to improvements to your trial, based on data as it becomes available. Adaptive designs are generally pre-specified and built into the initial trial design.

Examples of adaptive designs are group sequential designs, sample size re-estimation, enrichment designs, arm selection designs and adaptive allocation designs.

For a more detailed explanation of what adaptive clinical trials are, see the following video:
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Q. Why are adaptive design trials important and what potential advantages do they have?

Adaptive trials are seen by many to be a very valuable addition to clinical trial design toolkit as they give control to the trialist to improve a trial based on all the information as it becomes available. Adaptive design facilitates these improvements to a trial in a principled and pre-specified framework and thus can changes can be done without impacting trial legitimacy. This conceptually should allow our trial to be closer to optimal trial if the results had been known beforehand and thus give better and potentially more efficient inferences.

As a result, adaptive trials can decrease the costs involved in clinical trials by increasing success rates, allow greater flexibility in adding analyses and trial arms and allowing trials to end earlier if the results are either very promising or unpromising. This is of particular importance today as the success rate of clinical trials in general has become lower and the costs associated with clinical trials, particularly confirmatory phase II clinical trials, have escalated over the last 30 years.    

For a more detailed explanation of what the advantages of adaptive clinical trials are, see the following video:
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Q. What are the potential disadvantages of adaptive design?

Adaptive trials may also involve complex and different statistics and estimates than those commonly used in clinical trials and so may require specialized software and expertise to implement, which may incur additional costs up-front costs. For example, most adaptive designs used in clinical trials will require in-depth simulation to evaluate the design’s operating characteristics and expected Type I error rate. This may also mean results from an adaptive designs may not be directly comparable to those from a  fixed term trial. As a result certain inter-trial comparisons and meta-analysis may be difficult, which may cause problems from a regulatory point of view or for general understanding.

Adaptive trials will possibly incur additional logistical costs. Bias and unblinding are major issues as ensuring that the blinding is kept may incur additional costs and it is also a major risk to the integrity of the trial. As more people will be required to view the interim data as the trial progresses in order to make decisions on an adaptive basis then the situation arises where there is more scope for changes that could negatively impact the amount of bias in the trial. In large clinical trials, this will place more emphasis on working collaboratively with the relevant regulatory agency and the independent data monitoring committee (IDMC).

For a more detailed explanation of what the advantages and disadvantages of adaptive clinical trials are, see the following video:
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Q. Are Adaptive designs more efficient?

Adaptive designs allow clinical trials to be more flexible by utilising results accumulated in the trial to change the trial’s course. Trials with an adaptive design are usually more efficient, informative and can be more ethical than trials that have a traditional fixed design because they often make better use of resources such as time and money, and may require fewer participants.

Adaptive designs can also be potentially less efficient than a fixed term trial or simple adaptive design if designed poorly. For example, sample size re-estimation designs which lead to higher average sample sizes for minimal success rate increases or adaptive selection designs which include additional arms with minimal prior chance of succeeding. 

Overall, adaptive designs when properly considered and well-planned have considerable scope for increasing trial efficiency but the additional flexibility could mean more opportunities for making poor design decisions.

Q. What is a Group Sequential Design?

Group sequential designs are the most widely used type of adaptive trial in confirmatory Phase III clinical trials. Group sequential designs differ from a standard fixed term trial by allowing a trial to end early based on pre-specified interim analyses for efficacy or futility. Group sequential designs achieve this by using an error spending method which allows a set amount of the total Type I (efficacy) or Type II (futility) error at each interim analysis. The ability to end the trial can help reduce costs by creating an opportunity to get early approval for highly effective treatments and abandoning trials which have shown very poor results thus far. 

Q. What is the assessment of futility in clinical trials?

The term 'futility' refers to the inability of a clinical trial to achieve its aims, such as, ending a clinical trial when the interim results suggest that it is highly unlikely to achieve statistical significance. This can save resources which can then be used in other more promising studies. 

Q. What is sample size re-estimation (SSR)?

Sample size r-estimation (SSR) is a type of adaptive trial where one can change the sample size if required. Sample size determination is a pre-trial process which will be conducted on the basis of inherently uncertain planning parameters (e.g. variance, effect size) and thus changing the sample size based on improved interim estimates for these parameters is an obvious adaptation target. 

SSR can ensure that sufficient power is obtained for promising results in an underpowered study or could ensure more patients receive the superior treatment or transition directly from one trial phase to another. Combined this may reduce the use of resources and time or improve the likelihood of success of the trial. 

There are two primary types of SSR: Unblinded SSR and Blinded SSR. The main differences between these designs  being that they differ on whether the data is blinded or not and the planning parameter targeted to for an improved interim estimate. 

For a more detailed explanation of what SSR is, see the following video on sample size re-estimation:
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Q. What is blinded sample size re-estimation?

Blinded sample size re-estimation (SSR) design is a flexible design with the main purpose of allowing the sample size of a study to be reassessed mid-way into the study to ensure sufficient power without unblinding the interim data i.e. without allowing trialist know which treatment group interim data is from. 

As the effect size will be blinded, blinded SSR will typically target nuisance parameters used in the sample size determination such as the variance or control proportion. While the estimates for these nuisance parameters may be improved by using unblinded interim data, in blinded SSR designs this improvement is negligible against the best blinded estimate. However by keeping the blind, the logistical and regulatory barriers for adaption are significantly lowered as there is less chance of operational or statistical bias. 

For a detailed explanation of this topic, see the following video on blinded sample size re-estimation:
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Q. What is unblinded sample size re-estimation?

In unblinded sample size re-estimation the sample size is re-estimated at the interim analysis using unblinded data. As the interim data is unblinded, the interim effect is known and this is the typically target for unblinded SSR. Despite results from previous studies, the treatment effect can have a  high level of uncertainty at the design stage and thus the interim effect size is an obvious adaptation metric.

As unblinding creates significant risks for statistical and operational bias, unblinded sample size re-estimation is usually done in the context where an unblinded adaptive design is already planned, for example a design using the  common group sequential design. Due to this, the most common unblinded SSR designs are extensions to the group sequential design which add the option to increase the sample size in addition to option for early stopping.

The most common unblinded SSR framework assumes a design which powers initially for a more optimistic effect size but allows sample size increases for interim effect sizes which are less than the optimistic effect size but which are still “promising” for a smaller but still clinically relevant difference. For this reason, these designs are often called “promising zone” designs. 

To evaluate whether an interim result is “promising”, conditional power is the most common metric. However, some have suggested alternative metrics such as predictive power due to strong assumptions regarding the “true” effect size in conditional power calculations.

For a detailed explanation of this topic, see the following video on unblinbed sample size re-estimation:
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Q. What is conditional power?

Conditional power is the probability that the trial will reject the null hypothesis at a subsequent look given the current test statistic and the assumed “true”  parameter values, which are usually assumed to equal their interim estimates or their initial planning values. 

Q. What is predictive power?

Predictive power (also known as Bayesian Predictive Power) is the conditional power averaged over the posterior distribution of the effect size. It is commonly used to quantify the probability of success of a clinical trial. It has been suggested as a superior alternative to conditional power as it treats the “true” estimates as uncertain rather than fixed.

How does sample size affect hypothesis testing?

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How does changing the sample size affect the mean?

How does sample size affect results?